Daniele Puglisi

Department of Mathematics and Computer Sciences
University of Catania
Viale Andrea Doria, 6
I-95125 Catania CT

Office: 346
Office phone: ++39 095 7383055
Fax: ++39 095 330094

E-mail: dpuglisiunict.it

Research

In the paper

• P. Motakis, D. Puglisi, D. Zisimopoulou; A hierarchy of Banach spaces with C(K) Calkin algebras. To appear in Indiana Univ. Math. J. (2015)

the authors prove that for every countable compact metric space K there exists a Banach space X whose Calkin algebra is isomorphic, as a Banach algebra, to C(K).

Questions

• Does there exists a Banach space whose Calkin algebra is reflexive and infinite dimensional?
• Does there exists a Banach space whose Calkin algebra is isomorphic, as a Banach algebra, to C(K) for an uncountable compact space K?

Or more in general, it seem to be really interesting the following question

• Let A be a Banach algebra, does there exist a Banach space X so that the Calkin algebra of X is isomorphic, as a Banach algebra, to A?

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